God created the integers; all else is the work of man.
This is why we call the integers the natural numbers because they seem to be a work of nature rather than than an invention of man. But if one follows this thought, then one see's that this cannot possibly be correct. If God created the integers then he also created all other numbers - the reals, the imaginaries, the Lie algebras, the finite groups and so on. All of them are as natural as the integers. That we do not think so is merely that we are unfamiliar with them.
This position, whether you believe in God or not, is called mathematical Platonism. In fact, its such a truncated version of Platonism that its serious mistake to think this is what Platonism is about. But we are stuck with the name. In this notion numbers have ideal existences that are only accessible to the inner sense of the intellect. Here, numbets are unique and there are no copies. Although this notion to contemporary ears sounds bizarre and few mathematicians would give it credence, it is more or less how most mathematicians naively go about working with them.
The other main option is nominalism. Here the number three is understood, for example, to be about the collection of ALL three objects. This option became popular with the advent of set theory which is a theory of collections. Still, even this approach can be suspect since the unrestricted use of ALL as Russell pointed out leads to inconsistencies. Also, personally speaking, I think it unwieldy and not at all how I think of numbers and I suspect, pretty much everybody else. Its rather like describing a book as a collection of pages, which even if true, is only partially true, and doesn't get to the idea of a book as a thing in itself.
If you ascribe real essences to numbers then its of course wrong to think of 2 as an integer as different from 2 as a real. That people do so may seem from this point of view completely wrongheaded. Nevertheless, one can argue that they do so only as a manner of speaking and are actually focusing on different properties of the same thing because those are the properties that they are interested in - either in the pure mathematics sense where numbers are their own end - or practically because what they are modelling requires only those properties.